Refer to the rational number sense framework (introduced in Module 1). Analyse the following tasks and identify what types of number ideas are developed through an emphasis on (spatial) proportional reasoning. Connect the task to an appropriate content descriptor from the AC:M. Describe what types of gestures, materials / representations and spatial language could be used by both teachers and students to develop and communicate the ideas.
Activity 1. Here is a representation that shows the number birds that used my birdfeeder in my backyard, over four months. What do you notice? If this trend continues, how many birds will visit me in the fifth month? The tenth? Use the Cuisenaire rods to represent your thinking. (Note: picture needs to have horizontal lines removed)
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Activity 2. Penny’s chooks laid 30 eggs. She and her sister Sally, took three baskets to the shed to collect the eggs. Penny had the largest basket, and put 15 eggs in her to take back to the house. Sally split the remaining eggs equally between her two baskets. Sally was upset because she said she had to carry more eggs than Penny.
Activity 3. Grandma wanted to buy a new tablecloth. She likes orange and purple but wants a tablecloth that is more orange than purple. Are any of these tablecloths suitable?
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Activity 4. Harry and his friend Jack ordered a large pizza each for tea. Jack cut his pizza in half, and then half again, and ate three of the pieces. Harry only cut his pizza in half, but ate both pieces. Jack said that he ate more, because he ate three pieces and Harry only ate two. Is he correct? How do you know?
Activity 5. I started making a pattern of triangles out of pop sticks. I only have a total of 21 matchsticks. How many triangles can I make? Can you find a rule to explain the relationship between the number of triangles and number of sticks?
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